Devices for parting a continuously produced skein of sausages are already known for example from WO 03030646. With the known methods the skein is parted by tying off with, for example, two bar-shaped displacement elements, as illustrated in FIGS. 7a and 7b. Here, the displacement elements 8, 9 move towards one another and overlap, thereby shearing off the sausage skein 7. A disadvantage here is that no uniform support during displacement occurs, i.e. on tying off the sausage, and in particular when parting takes place simultaneously. Diagonal squashing of the parting point occurs, as can be seen in FIG. 7b. The displacement shears produce a sausage end which is misshapen on the side facing away from the displacement shears and is not closed off by the sausage sleeve. This is disadvantageous for the ensuing processes, such as for example smoking or roasting, because roast material can be emitted at this point. The above problems occur in particular with relatively soft sausage sleeves, such as for example sausage sleeves which are coextruded during the sausage production and have not yet become completely firm during tying off and parting. This type of coextrusion method is for example known from EP 1 371 293.